An example of an almost greedy uniformly bounded orthonormal basis for \(L_p(0,1)\)

DOI10.1016/j.jat.2007.04.011zbMath1146.46006arXivmath/0611890OpenAlexW1976377965MaRDI QIDQ2481484

Morten Nielsen

Publication date: 10 April 2008

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611890

zbMATH Keywords

Schauder basisquasi-greedy basisalmost greedy basisdecreasing rearrangementsbounded orthonormal systems

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items

Lebesgue-type inequalities in greedy approximation, Efficiency of weak greedy algorithms for \(m\)-term approximations, Fundamental functions of almost greedy bases of \(L_p\) for \(1<p< \infty\), Sparse Approximation by Greedy Algorithms, Nonlinear approximation by renormalized trigonometric system, Quasi-greedy bases in \(\ell_p\) (\(0 < p < 1\)) are democratic, On certain subspaces of \(\ell_p\) for \(0 < p \le 1\) and their applications to conditional quasi-greedy bases in \(p\)-Banach spaces, SPARSE APPROXIMATION AND RECOVERY BY GREEDY ALGORITHMS IN BANACH SPACES

Cites Work

• The best \(m\)-term approximation and greedy algorithms
• Greedy algorithm and \(m\)-term trigonometric approximation
• The thresholding greedy algorithm, greedy bases, and duality
• Convergence and Divergence of Decreasing Rearranged Fourier Series
• Note on Decreasing Rearrangement of Fourier Series
• Greedy algorithm for general biorthogonal systems
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